arXiv subjects

Artur Ziviani

Publications and source records attributed to Artur Ziviani.

25 records · Page 2Linked to original sources

arXiv2016

MultiAspect Graphs: Algebraic representation and algorithms

We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property of being isomorphic to a directed graph. In particular, we show that, as a consequence of the properties associated with the MAG structure, a MAG can be represented in matrix form. Moreover, we also show that any possible MAG function (algorithm) can be obtained from this matrix-based representation. This is an important theoretical result since it paves the way for adapting well-known graph algorithms for application in MAGs. We present a set of basic MAG algorithms, constructed from well-known graph algorithms, such as degree computing, Breadth First Search (BFS), and Depth First Search (DFS). These algorithms adapted to the MAG context can be used as primitives for building other more sophisticated MAG algorithms. Therefore, such examples can be seen as guidelines on how to properly derive MAG algorithms from basic algorithms on directed graph. We also make available Python implementations of all the algorithms presented in this paper.

cs.DM↗

arXiv2016

On MultiAspect Graphs

Different graph generalizations have been recently used in an ad-hoc manner to represent multilayer networks, i.e. systems formed by distinct layers where each layer can be seen as a network. Similar constructions have also been used to represent time-varying networks. We introduce the concept of MultiAspect Graph (MAG) as a graph generalization that we prove to be isomorphic to a directed graph, and also capable of representing all previous generalizations. In our proposal, the set of vertices, layers, time instants, or any other independent features are considered as an aspect of the MAG. For instance, a MAG is able to represent multilayer or time-varying networks, while both concepts can also be combined to represent a multilayer time-varying network and even other higher-order networks. Since the MAG structure admits an arbitrary (finite) number of aspects, it hence introduces a powerful modelling abstraction for networked complex systems. This paper formalizes the concept of MAG and derives theoretical results useful in the analysis of complex networked systems modelled using the proposed MAG abstraction. We also present an overview of the MAG applicability.

cs.DM↗

arXiv2015

A Unifying Model for Representing Time-Varying Graphs

Graph-based models form a fundamental aspect of data representation in Data Sciences and play a key role in modeling complex networked systems. In particular, recently there is an ever-increasing interest in modeling dynamic complex networks, i.e. networks in which the topological structure (nodes and edges) may vary over time. In this context, we propose a novel model for representing finite discrete Time-Varying Graphs (TVGs), which are typically used to model dynamic complex networked systems. We analyze the data structures built from our proposed model and demonstrate that, for most practical cases, the asymptotic memory complexity of our model is in the order of the cardinality of the set of edges. Further, we show that our proposal is an unifying model that can represent several previous (classes of) models for dynamic networks found in the recent literature, which in general are unable to represent each other. In contrast to previous models, our proposal is also able to intrinsically model cyclic (i.e. periodic) behavior in dynamic networks. These representation capabilities attest the expressive power of our proposed unifying model for TVGs. We thus believe our unifying model for TVGs is a step forward in the theoretical foundations for data analysis of complex networked systems.

cs.DS↗

arXiv2015

Time Centrality in Dynamic Complex Networks

There is an ever-increasing interest in investigating dynamics in time-varying graphs (TVGs). Nevertheless, so far, the notion of centrality in TVG scenarios usually refers to metrics that assess the relative importance of nodes along the temporal evolution of the dynamic complex network. For some TVG scenarios, however, more important than identifying the central nodes under a given node centrality definition is identifying the key time instants for taking certain actions. In this paper, we thus introduce and investigate the notion of time centrality in TVGs. Analogously to node centrality, time centrality evaluates the relative importance of time instants in dynamic complex networks. In this context, we present two time centrality metrics related to diffusion processes. We evaluate the two defined metrics using both a real-world dataset representing an in-person contact dynamic network and a synthetically generated randomized TVG. We validate the concept of time centrality showing that diffusion starting at the best classified time instants (i.e. the most central ones), according to our metrics, can perform a faster and more efficient diffusion process.

cs.SI↗

arXiv2014

DANCE: A Framework for the Distributed Assessment of Network Centralities

The analysis of large-scale complex networks is a major challenge in the Big Data domain. Given the large-scale of the complex networks researchers commonly deal with nowadays, the use of localized information (i.e. restricted to a limited neighborhood around each node of the network) for centrality-based analysis is gaining momentum in the recent literature. In this context, we propose a framework for the Distributed Assessment of Network Centralities (DANCE) in complex networks. DANCE offers a single environment that allows the use of different localized centrality proposals, which can be tailored to specific applications. This environment can be thus useful given the vast potential applicability of centrality-based analysis on large-scale complex networks found in different areas, such as Biology, Physics, Sociology, or Computer Science. Since the localized centrality proposals DANCE implements employ only localized information, DANCE can easily benefit from parallel processing environments and run on different computing architectures. To illustrate this, we present a parallel implementation of DANCE and show how it can be applied to the analysis of large-scale complex networks using different kinds of network centralities. This implementation is made available to complex network researchers and practitioners interested in using it through a scientific web portal.

cs.NI↗

arXiv2011

Distributed Algorithm to Locate Critical Nodes to Network Robustness based on Spectral Analysis

We propose an algorithm to locate the most critical nodes to network robustness. Such critical nodes may be thought of as those most related to the notion of network centrality. Our proposal relies only on a localized spectral analysis of a limited subnetwork centered at each node in the network. We also present a procedure allowing the navigation from any node towards a critical node following only local information computed by the proposed algorithm. Experimental results confirm the effectiveness of our proposal considering networks of different scales and topological characteristics.

cs.NI↗

arXiv2010

Capacity Planning for Vertical Search Engines

Vertical search engines focus on specific slices of content, such as the Web of a single country or the document collection of a large corporation. Despite this, like general open web search engines, they are expensive to maintain, expensive to operate, and hard to design. Because of this, predicting the response time of a vertical search engine is usually done empirically through experimentation, requiring a costly setup. An alternative is to develop a model of the search engine for predicting performance. However, this alternative is of interest only if its predictions are accurate. In this paper we propose a methodology for analyzing the performance of vertical search engines. Applying the proposed methodology, we present a capacity planning model based on a queueing network for search engines with a scale typically suitable for the needs of large corporations. The model is simple and yet reasonably accurate and, in contrast to previous work, considers the imbalance in query service times among homogeneous index servers. We discuss how we tune up the model and how we apply it to predict the impact on the query response time when parameters such as CPU and disk capacities are changed. This allows a manager of a vertical search engine to determine a priori whether a new configuration of the system might keep the query response under specified performance constraints.

cs.IR↗